Stability and Stabilization of Heterogeneous Switched Systems with Mode-Dependent Average Dwell Time via Homogeneous Polynomial Lyapunov Functions Approach

This work researches the problem of searching for multiple homogeneous polynomial Lyapunov functions (HPLFs) for heterogeneous switched linear systems. First, a nonconvex optimization condition is constructed to study the stability property of heterogeneous switched systems, where each Lyapunov function candidate reduces dimension to their corresponding matrix eigenvalue. Based on the stability analysis condition, a controller-dependently multiple HPLFs condition is introduced to determine controllers and explores locally minimum mode-dependent average dwell time (LMMDADT). Additionally, the existing properties condition and solvable properties condition of controllers are given in the form of HPLFs. At last, a practical example and a contrast example are both presented to show feasibility of the proposed results.